We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.
We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.
In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. Motivated by this perspective, we study a minimal compact U(1) lattice gauge model describing a spin chain coupled to two-dimensional Dirac conduction electrons. The spin chain is described by fermionic partons carrying spin and U(1) gauge charge. The heavy-fermion quasiparticle is a bound state of a U(1) matter field carrying unit electric charge and U(1) gauge charge, and the fermionic parton. Using sign-problem-free determinant quantum Monte Carlo simulations, we identify two symmetry-equivalent regimes: a heavy-fermion metal with a sharp composite-fermion resonance and robust low-frequency transport, and a Kondo-breakdown metal with an incoherent resonance and vanishing low-frequency transport. For any finite lattice extent in the direction perpendicular to the chain, the Luttinger volume of the heavy-fermion phase counts both composite and conduction electrons, while in the Kondo-breakdown phase it counts only the conduction electrons. The evolution of the composite-fermion spectrum, dynamical spin structure factor, and optical conductivity provides a nonperturbative demonstration of gauge-mediated Kondo breakdown and establishes transport fingerprints of an orbital-selective Mott transition in the context of U(1) gauge theories of heavy fermions.
Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (Nf) and the strength of gauge fluctuations is mapped out. Here we focus on the large fermion flavor case (Nf=8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED3-Gross-Neveu chiral O(2) universality whose properties are still largely unknown.
We explore a Z2 Hamiltonian lattice gauge theory in one spatial dimension with a coupling h, without imposing any Gauss' law constraint. We show that in our model h=0 is a free deconfined quantum critical point containing massless fermions where all Gauss' law sectors are equivalent. The coupling h is a relevant perturbation of this critical point and fermions become massive due to confinement and chiral symmetry breaking. To study the emergent Gauss' law sectors at low temperatures in this massive phase we use a quantum Monte Carlo method that samples configurations of the partition function written in a basis in which local conserved charges are diagonal. We find that two Gauss' law sectors, related by particle-hole symmetry, emerge naturally. When the system is doped with an extra particle, many more Gauss's law sectors related by translation invariance emerge. Using results in the range 0.01<h≤0.15 we find that three different mass scales of the model behave like hp where p≈0.579.
Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
The problem of a U(1) U ( 1 ) gauge field coupled to fermions in (2+1) dimensions is of fundamental importance, as it is believed to give rise to U(1) U ( 1 ) Dirac spin liquid (DSL) state in quantum magnets and the strongly coupled conformal field theory in quantum electrodynamics. However, numerical progress has long been hampered by the steep computational cost of traditional determinant quantum Monte Carlo (QMC). Here, we develop a GPU-accelerated hybrid QMC algorithm assisted with several novel technical improvements, which significantly reduces the complexity to be linear with respect to space-time volume, and scales the simulation up to an unprecedented size. At this scale, we observe asymptotic convergence of fermion bilinear correlator and conserved current correlator, which was unclear previously, and find their scaling dimensions in good agreement with field theory, which supports the conformal nature of the Dirac spin liquid. Our advances establish a scalable framework to study DSL physics and its transitions at larger scales.
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.
Monte Carlo simulations of strongly interacting fermionic systems are plagued by the fermion sign problem, making the nonperturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of fermion flavors, challenging. Moreover, typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on the meron cluster algorithm, which can solve the fermion sign problem in a class of models without involving the determinant. We develop and benchmark new meron algorithms to simulate fermions coupled to Z2 and U(1) gauge fields in the presence of appropriate four-fermi interactions. Such algorithms can be used to uncover potential exotic properties of matter, particularly relevant for quantum simulator experiments. We demonstrate the emergence of the Gauss’ law at low temperatures for a U(1) model in (1+1)D . Published by the American Physical Society 2024